Geometry - Question Bank - Q6

[guilopes]

Is quadrilateral ABCD a rectangle?

(1) Line segments AC and BD bisect one another.

(2) Angle ABC is a right angle.

The correct answer according to the explanation is answer C.

I answered E, however, since I understood the quadrilateral can also be a square.

Did I miss something? Is (by definition) a square one kind of rectangle?

[Sage Pearce-Higgins]

Yes, a square is a special kind of rectangle. Just as a rectangle is a special kind of quadrilateral. Can you describe the relationship between a parallelogram, a rhombus, and a trapezium as well?

[guilopes]

Let´s see.

Parallelogram: Opposite sides and angles are equal.

Rhombus: Diagonals are always perpendicular bisectors.

Trapezoid: One pair of opposite sides is parallel. Area = avg ((inf + sup)*h)/2

[Sage Pearce-Higgins]

Those statements are true (although that's not a definition of a rhombus: all rhombuses do have diagonals that are perpendicular bisectors, but not all perpendicular bisectors are diagonals of rhombuses). But I asked about the relationship between the different shapes.

[guilopes]

I think so.

Parallelogram is a quadrilateral in which:

- Each two opposite sides are parallel and equal in lenght
- Each two opposite angles are equal in measure
- The sum of consecutive angles equals 180 degrees
- The two diagonals bisect each other

Rectangle is a parallelogram with one right angle and:
- All angles are right
- The two diagonals are equal in length

Rhombus is a parallelogram in which two adjacent sides are equal in lentgh
- The sides are equal in length
- The two diagonals are perpendicular

Square is a rectangle in which two adjacent sides are equal in length or is a rhombus with a right angle
- The four sides are equal in length
- The two diagonals are equal in length and are perpendicular

[Sage Pearce-Higgins]

Good job. So, you can see that a parallelogram is a special kind of trapezoid; a rhombus is a special parallelogram; a square is a special rhombus; a rectangle is a special parallelogram; a square is a special rectangle. Phew!

[guilopes]

Thank you!

[Sage Pearce-Higgins]